The present invention relates to a method and apparatus employing the wavelet transform for image compression, and more particularly relates to the scanning sequence of the output of the wavelet transform.
Image compression methods using the discrete cosine transform have been standardized by the Joint Photographic Experts Group (JPEG) and the Moving Picture Experts Group (MPEG). These methods divide an image into blocks, execute a discrete cosine transform on each block, quantize the resulting coefficients, rearrange the coefficients in a zigzag scanning sequence that tends to collect most of the zero coefficients at the end of each block, and then encodes the coefficients by a variable-length coding scheme in which a single codeword represents either a terminal string of consecutive zero coefficients, or a non-zero coefficient and the preceding zero coefficients, wherein the length of the codeword decreasing as the magnitude of the non-zero coefficient decreases and as the number of preceding zeros decreases.
Recently, however, there has been much interest in alternative image compression methods that use the wavelet transform. The wavelet transform iteratively separates low spatial frequencies from high spatial frequencies to produce a multiresolution representation of an image. For many images, the wavelet transform offers the possibility of a higher compression ratio than the discrete cosine transform.
The output of the wavelet transform can be compressed by the same quantization, zigzag scanning, and encoding steps used to compress the output of the discrete cosine transform, but for the wavelet transform, the zigzag scanning sequence is not ideal. Instead of collecting zero values at the end of each block, the zigzag scanning sequence tends to intermingle the zero values and non-zero values, which impairs the coding efficiency.